A leader’s mistakes echo louder, so own them louder too.

Whatever position you hold amplifies what you do, mistakes included, because more people saw it and more people will repeat it. That means a quiet or partial apology does not travel as far as the error did. Owning it at full volume is not self-punishment. It matches the correction to the size of the original signal, and it shows everyone what to do with their own mistakes.

If you got something wrong in front of people, fix it in front of the same people. Say what you did without softening the verb. Then say what you are doing instead, and do not bring it up again.